A canonical construction for nonnegative integral matrices with given line sums

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Abstract

Let p be a positive integer and let A((p)) (R, S) be the class of nonnegative integral matrices with entries less than or equal to p, with row-sum partition R, and column-sum partition S. In this paper we state a new necessary and sufficient condition for A((p)) (R, S) not equal empty set. This condition generalizes the well known Gale-Ryser theorem. We also present a canonical construction for matrices in A((p)) (R, S).
Original languageEnglish
Pages (from-to)304-321
JournalLinear Algebra and Its Applications
Volume484
DOIs
Publication statusPublished - 2015

Keywords

  • Algorithm
  • Integral matrices with given lines
  • Partition domination

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